Error

Derivation

1. Initial program 0.1

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

2. Initial simplification0.1

   \[\leadsto \frac{e \cdot \sin v}{(\left(\cos v\right) \cdot e + 1)_*}\]
3. Using strategy rm

4. Applied add-sqr-sqrt0.2

   \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*} \cdot \sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}\]

5. Applied associate-/r*0.2

   \[\leadsto \color{blue}{\frac{\frac{e \cdot \sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}\]
6. Using strategy rm

7. Applied *-un-lft-identity0.2

   \[\leadsto \frac{\frac{e \cdot \sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}{\color{blue}{1 \cdot \sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}\]

8. Applied *-un-lft-identity0.2

   \[\leadsto \frac{\frac{e \cdot \sin v}{\color{blue}{1 \cdot \sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}}{1 \cdot \sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

9. Applied times-frac0.2

   \[\leadsto \frac{\color{blue}{\frac{e}{1} \cdot \frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}}{1 \cdot \sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

10. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{\frac{e}{1}}{1} \cdot \frac{\frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}\]

11. Simplified0.2

    \[\leadsto \color{blue}{e} \cdot \frac{\frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

12. Simplified0.1

    \[\leadsto e \cdot \color{blue}{\frac{\sin v}{(\left(\cos v\right) \cdot e + 1)_*}}\]

13. Final simplification0.1

    \[\leadsto e \cdot \frac{\sin v}{(\left(\cos v\right) \cdot e + 1)_*}\]

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))